Oily Water

Normal sudoku rules apply.

Digits in cages do not repeat and must sum to the small clue, if given.

Each cage is either full of "oil" (even digits), full of "water" (odd digits), or a mix of both. In all cases, each "row" within a cage is of just one type (oil or water). Oil floats on water, so even digits will always be in rows above odd digits in mixed cages.

The nine letters (OILY WATER) map one-to-one with the nine digits (1 - 9). The solver must deduce which is which.